PORTUGALIAEMATHEMATICA
Vol. 59, No. 3, pp. 335-349 (2002)
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PORTUGALIAE MATHEMATICA Vol. 59, No. 3, pp. 335-349 (2002) |
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Kuramoto--Sivashinsky Equation in Domains with Moving BoundariesAlfredo Tadeu Cousin and Nickolai Andreevitch LarkineDepartment of Mathematics, State University of Maringá,Av. Colombo, 5790 -- CEP: 87020-900, Maringá, PR -- BRAZIL E-mail: atcousin@uem.br The Institute of Theoretical and Applied Mechanics, Novosibirsk -- 90, 630090 -- RUSSIA E-mail: nalarkin@dma.uem.br Abstract: In the non-cylindrical domain ${Q}=\{(x,t); \alpha_1(t)<x<\alpha_2(t), t\in(0,T)\}$ we consider the initial-boundary value problem for the one-dimensional Kuramoto--Sivashinsky equation $$ u_t+u\,u_x+\beta\,u_{xx}+\delta\,u_{xxxx}=0. $$ We prove the existence and uniqueness of global weak, strong and smooth solutions. The exponential decay of the solutions is also proved. Keywords: Kuramoto--Sivashinsky equation; noncylindrical domains; Galerkin method. Classification (MSC2000): 35Q35, 35Q53. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2002 Sociedade Portuguesa de Matemática
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